The necessity to include random fluctuations (such as thermal noise) into the dynamics of magnetisation has been conjectured by physicists for many years (see for example [1]}, [2]}, [3]}. The existence and uniqueness of solutions for the Landau-Lifshitz equation without the Slonczewski term but including random fluctuations was intensely studied in recent years [4]}, [5]}, [6]}.
